Willetts had earlier sought to stress that the move would free up more publicly subsidised places for undergraduates from poorer homes and improve social mobility.

But critics said the move would entrench privilege and turn back the clock to a time when "breeding not brains" mattered, with the Liberal Democrat MP and party president, Tim Farron, warning that he would oppose any measure that gave the appearance of increasing university access for the rich.

Downing Street swiftly distanced itself from any suggestion that it was backing plans for students with rich parents be given priority access to university as a way of expanding the overall number of university places and university income.

No 10 did not rule out a limited version of the idea appearing in the university white paper, due this summer, but stressed that no proposal would be backed if it reduced social mobility.

"We are listening to proposals about what we would do in the white paper to ensure we improve access to higher education," a No 10 spokesman said.

The business secretary, Vince Cable, said he was willing to look at how to expand off-quota places through company sponsorships, but stressed that he did not support the children of the rich being given priority access to university.

By lunchtime, Willetts had issued a statement to insist there was "no question" of wealthy students being able to buy a place at university. "Access to a university must be based on ability to learn not ability to pay," the universities minister said.

Under current government plans, annual student numbers are capped to keep costs down, with English universities allowed to charge UK students a maximum annual fee of £9,000 from 2012, which graduates do not have to start paying until they are earning £21,000 a year.

Willetts sparked controversy when he suggested in an interview with the Guardian that universities could increase the numbers of British students by charging some the full annual fees of up to £28,000 a year for the most expensive courses, payable up front, who would not then require the support of the taxpayer.

The changes would give more students the chance to attend their first choice university, a suggestion that many see as enabling the children of the wealthiest parents to buy their way in.

The move is being considered at a time when the government is cutting 10,000 publicly funded university places.

Employers and charities will also be encouraged to sponsor off-quota places under the plans to be outlined in the white paper.

Earlier in the day, Willetts had told the BBC Radio 4 Today programme: "People are coming to us with innovative ideas about how you could liberalise the system so it was possible for extra people to get to university.

"These are people who we wish to go to university and who, sadly, are being turned away at the moment just because there aren't enough places.

"We would need to have a set of criteria, if this went ahead, that absolutely passed muster as improving social mobility.

"I start from the view that, by and large, more people going to university is a good thing for social mobility. Anything that we did if this does go forward would have to pass the test of improving social mobility, not reversing it."

In a sign of the Liberal Democrats' determination to assert more directly their differences with the Conservatives following the elections debacle, Farron, the MP for Westmorland and Lonsdale, said higher education should be "free at the point of use" for everyone who can benefit from university.

The MP – whose party took a hit at the polls last Thursday for the party's U-turn on tuition fee rises – told BBC News any proposal that looked like increasing university access for the rich would not get his backing.

"If that is the case, then that would be completely wrong and I would be against such a move," he said. "If it's about making sure we increase places for people of poorer backgrounds, that's something that's worth looking at.

"The real difficulty – one of the reasons why I voted against the fee rise last year – is not so much the unfairness of the package but how it appears to people out there."

Farron added: "Higher education should be free at the point of use and that people who are able to benefit from a university education should be able to do so.

"I hugely regret there are tuition fees at all, never mind the higher ones we currently have. It's right that we should explore ways that people from less well-off backgrounds [can] have the best possible access to higher education."

The UCU general secretary, Sally Hunt, said: "Far from increasing social mobility, it is hard to see how this is anything other than the government entrenching privilege for the wealthy in response to its failing university fees policy.

"We risk turning the clock back to a time when breeding rather than brains were required to get on in life. The news is particularly embarrassing for the Liberal Democrats as all their MPs pledged to vote, and campaign, against higher fees."

Aaron Porter, president of the National Union of Students (NUS), said the move would create a "two-tier system" in university education.

"The government is yet again tossing out a poorly conceived policy idea in an attempt to disguise the chaos it has created in university funding and the shortfall in finances that has created," he said.

"This creates a two-tier system that allows the richest, less able applicants a second bite at the university cherry and denies low- and middle-income students the same opportunity."

John Denham, the shadow business secretary, who has raised the issue in an urgent question in the Commons this afternoon, said low-income teenagers would have no chance of getting the extra university places created by Willetts's latest plan.

Willetts denied suggestions that the scheme would allow less qualified applicants to get to a good university by the backdoor.

"I don't think that would be fair," he told Today. "That's why one of the crucial criteria would be that people have to have the same high academic standards."

Willetts later issued a clarifying statement, saying: "We will only consider allowing off-quota places where it contributes to the coalition commitment to improve social mobility and increase fair access.

"There is no question of wealthy students being able to buy a place at university. Access to a university must be based on ability to learn not ability to pay."

He added: "We have been discussing the idea of charitable donors and employers endowing additional places on a needs-blind basis which will be a subject for consultation in the higher education white paper."

The proposal is most likely to be taken up by highly selective institutions, which turn away thousands of qualified candidates a year. Oxford accepted slightly more than 3,000 British and EU undergraduates out of about 17,000 who applied for the current academic year.

That demand is due to intensify as the latest application figures show the number of candidates for this autumn has risen by 2.1% to about 633,000 – another record high.

The places may not be covered by access agreements, under which universities are required to outline how they will improve their proportion of students from state schools and deprived backgrounds.

Under one version of the scheme, universities might operate a "needs-blind" admissions process, which assesses all candidates regardless of their ability to pay, but then offers places off-quota to candidates from the most privileged homes.

The expansion of places will put greater pressure on less popular universities. Ministers have warned that undersubscribed institutions could have government-funded places withdrawn.